Global Navigation Satellite System (GNSS)-based continuous and accurate train positioning is one of the key technologies for advanced train operations such as train virtual coupling. However, GNSS-based train positioning faces significant challenges in real-world scenarios due to environmental complexities and signal interferences. Considering this issue, this paper presents an approach for modeling and performance analysis of GNSS-based train positioning systems using Colored Petri Nets (CPNs). By systematically modeling the GNSS signal reception and processing process, the performance of the positioning system under various environment scenarios is evaluated. The system model integrates three types of interference signals (i.e., Amplitude Modulation (AM) signals, Frequency Modulation (FM) signals, and pulse signals) while incorporating environmental factors such as terrain obstructions and tunnel shielding. Additionally, the Extended Kalman Filter (EKF) algorithm is employed to process GNSS observation data, providing accurate train position estimations. The simulation results demonstrate that signal interferences and complex environmental conditions significantly affect the GNSS-based positioning accuracy. This study offers a comprehensive framework for evaluating the performance of GNSS-based train positioning systems in different scenarios, highlighting critical factors that influence positioning accuracy and stability.